Definition of a Relation and a Function

 

Relation:  A relation is simply a set of ordered pairs.

  The first elements in the ordered pairs, the x-values, form the domain.  The second elements in the ordered pairs, the y-values, form the range.

This mapping shows a relation from set A into set B.  The relation consists of the ordered pairs
(1,8), (1,2), (3,9), (7,9), and (12,16).
The domain is the set {1, 3, 7, 12}
The range is the set {2, 8, 9, 16}.
The range is the dependent variable.

 

Function:  A function is a set of ordered pairs in which each element of the domain has only ONE element associated with it in the range.

  The relation shown above is NOT a function because the element 1 (in the domain) is mapped to two elements in the range, 8 and 2.

  A function may have two x-values assigned to the same y-value, but may not have two y-values assigned to the same x-value.

  Real-life items can be thought of as possessing the properties of a function.  Pricing in a store could be described as a function since every pair of identical items in the store must cost the same amount.

 


Roberts